Forty-eight percent of adults favor the project, while 50 percent oppose it, according to the poll. Opposition is even greater among likely voters, 54 percent to 43 percent.

In addition to division over high-speed rail, a majority of likely voters -- 51 percent -- oppose an $11.1 billion water bond scheduled for the November 2014 ballot. The bond, tied politically to Gov. Jerry Brown's effort to build two water-diverting tunnels through the Sacramento-San Joaquin Delta, includes funding for dams, wastewater treatment and other water infrastructure projects.

The Legislature has withdrawn the bond from two previous elections, and Brown has urged lawmakers to reduce its cost.

When people who oppose the water bond are asked how they would vote if it cost less, overall support increases among likely voters to 55 percent, with 38 percent opposed, according to the poll.

The poll comes amid lingering concerns about the economy and state spending.

A plurality of Californians -- 45 percent -- named jobs and the economy as the most important issue facing the state, according to the poll. They are divided about whether they expect good economic times or bad economic times in the next year, 44 percent to 49 percent, respectively.

Brown's public approval rating among California adults slipped two percentage points from January, to 49 percent. The Legislature's public approval rating held flat at 34 percent.

Sixty-five percent of Californians say the state budget situation is still a big problem, according to the poll.